Class 06 PROJECT MAGIC SQUARE

 Class 06

PROJECT 1- MAGIC SQUARE

Objective :

 To study the principles and formation of magic squares.

Description : 

A magic square is a square array of numbers 1,2,3,4,5….n arranged in such a way that the sum of each row, each column and both diagonals is constant.

Procedure : 

let us develop a magic square.

 Example 1

STEP 1 : Choose any number to start to fill the magic square.

STEP 2 :Let us start from 1 to 16 numbers to fill the square.

STEP 3: All the numbers 1,2,3,4,5,6,7,8,……..16 are written in order from left to right across each row in turn starting from the top left hand corner.

 STEP 4:  Numbers are then interchanged diagonally by opposite numbers. 

PROJECT 1 – KNOWING OUR NUMBERS

Example 2

STEP 1 : Here we choose the numbers from 5 to 20 and make a magic square.

STEP 2 : Fill all the numbers starting from 5, 6, 7, 8 --- 20 in order from left to right across each row in turn, starting from the top left hand corner. (Figure 3).

STEP 3 : Numbers are then interchanged diagonally by opposite numbers.

STEP 4 : We get a magic square of sum of numbers in each row, each column and each diagonal is 50. 

Cup Method

STEP 1 : Write all the 16 numbers from 1 to 16 as shown in figure which seem to be in two cups.

STEP 2 : Number 1 to 8 are written in an open cup and 9 to 16 are written in an inverted cup.

PROJECT 1 – KNOWING OUR NUMBERS

STEP 3 : Now invert the middle rows as shown in the figure.

STEP 4 : The sum of numbers in each row, each column and each diagonal is 34.

STEP 5 :  We can also observe some more interesting facts in this magic square.

(i) The sum of central square is also 34.

(ii) The sum of corner elements of square is also 34.

You can make your own magic squares the same way.